About This Chapter
Continuous Probability Distributions - Chapter Summary and Learning Objectives
Continue your study of probability distributions with this chapter on continuous random variables and normal distribution. Through a series of short, engaging video lessons, our instructor shows you how these concepts and their graphs can be used to calculate area and estimate population percentages, among other applications. By the end of this chapter, you should be able to do the following:
- Find expected values of continuous probability distributions
- Use the normal distribution to find probabilities
- Determine the z-score of a normal distribution
- Link to Table: Z-Scores & Standard Normal Curve Areas Table
|Graphing Probability Distributions Associated with Random Variables||Demonstrate steps for plotting a random variable's probability distribution.|
|Finding & Interpreting the Expected Value of a Continuous Random Variable||Outline methods for using probability distributions to find a continuous random variable's expected values.|
|Developing Continuous Probability Distributions Theoretically & Finding Expected Values||Learn how to find expected values of a continuous random variable using theoretical probability distributions.|
|Probabilities as Areas of Geometric Regions: Definition & Examples||Demonstrate how probabilities can be used to calculate area.|
|Normal Distribution: Definition, Properties, Characteristics & Example||Illustrate the properties and characteristics of normal distributions.|
|Finding Z-Scores: Definition & Examples||Outline the steps taken to identify the relationship between an individual score and a group's mean score.|
|Estimating Areas Under the Normal Curve Using Z-Scores||Use z-scores to estimate the areas under a normal curve.|
|Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples||Describe the process of estimating percentages using normal distributions and the empirical rule.|
|Using the Normal Distribution: Practice Problems||Complete a series of sample problems to practice finding probabilities using the normal distribution.|
|Using Normal Distribution to Approximate Binomial Probabilities||Demonstrate how to approximate binomial probabilities using the normal distribution.|
|How to Apply Continuous Probability Concepts to Problem Solving||Learn how to solve problems using continuous probability concepts.|
1. Graphing Probability Distributions Associated with Random Variables
What's a random variable? Does it have anything to do with gambling? What's the difference between a continuous and a discrete variable? This lesson explains the difference and how to graph each one.
2. Finding & Interpreting the Expected Value of a Continuous Random Variable
How can you find the expected value of something like height distributions? This lesson explains how to find and interpret the expected value of a continuous random variable.
3. Developing Continuous Probability Distributions Theoretically & Finding Expected Values
What is an expected value? How can you tell how many time you should expect a coin to land on heads out of several flips? This lesson will show you the answers to both questions!
4. Probabilities as Areas of Geometric Regions: Definition & Examples
In this lesson, you're going to learn what a random variable is and examine core concepts related to probabilities as areas of geometric regions and expected values of probability distributions.
5. Normal Distribution: Definition, Properties, Characteristics & Example
In this lesson, we will look at the Normal Distribution, more commonly known as the Bell Curve. We'll look at some of its fascinating properties and learn why it is one of the most important distributions in the study of data.
6. Finding Z-Scores: Definition & Examples
Talking about multiples of standard deviations can get exhausting and confusing. Luckily, z-scores allow us to talk about how far a point is removed from a mean in terms of how many standard deviations away it is.
7. Estimating Areas Under the Normal Curve Using Z-Scores
So now that we have a Z-score, what is it used for? Sure, it can make your life easier when describing standard deviations, but finding the area under the normal curve is where the Z-score shines.
8. Estimating Population Percentages from Normal Distributions: The Empirical Rule & Examples
If you've been working with z-scores for long, you probably get tired of checking those tables every time you need to check the area under the curve. Luckily, the empirical rule helps us memorize the most important values.
9. Using the Normal Distribution: Practice Problems
In this lesson, we will put the normal distribution to work by solving a few practice problems that help us to really master all that the distribution, as well as Z-Scores, have to offer. Review the concepts with a short quiz at the end.
10. Using Normal Distribution to Approximate Binomial Probabilities
Binomial probabilities describe processes in our world. Learn how to create and interpret a binomial probability distribution graph, and discover how the normal distribution can form a good approximation of the binomial distribution.
11. How to Apply Continuous Probability Concepts to Problem Solving
Continuous probability distributions can be a good approximation of many real world processes and phenomena. In this lesson, you will gain a conceptual understanding of continuous probability distributions and how to apply their properties to solve problems.
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